Cheating. Possibly lying. But also polyamory.

The appropriate label to use is the one that best describes what the people in the relationship have agreed to, implicitly or explicitly. Cheating doesn't turn a monogamous relationship into something else, it's just a violation of the relationship's rules. Ditto with a polyamorous one.

And this does happen, by the way, and when it does, it's usually really awful. Monogamous cheating is bad enough, but when you're in a triad (or a quad, or...) you do at least as much damage to several people. More, probably, considering that there's usually more trust and clear negotiation involved.